I see why you would want a different notation for I1. However, I would not change I1 as I change the figure. Although they are different currents, they refer to the same resistor R1. The circuit changes, as the figures show, so the current through R1 changes.

Thank you for your comments.
1. I do not see that typo. Maybe you have an old version of this article?
2. As you say in your second post, you found the answer.

I1 first time is when R2 is out of circuit.. The second I1 is the original I1 of first circuit when the R2 is put back in the circuit.

This is not so clear in the text. Why not to call them I1′ and I1 and I2′ and I2 etc..

Thank you again

Antonio

Few remarks:

1-There is an error-typo when you write “there are two way to find R1” which should read “there are two ways to find I1”

2-Why do you find two different values for each I1, I2, I3 and I4 ? First time you say “After calculation we find… I1 = “0.176 mA”… and later “I1=-0.112 mA” ? Did I get you wrong ?

Brgds
Antonio